Saw chains may experience excess vibration, which can be translated to a user. Such vibrations may be caused by a variety of factors, including when the cutter link contacts a portion of an article to be cut that is harder than the surrounding portions. Attempts have been made to minimize vibration. These attempts have focused on using a cutter link and tie strap configuration that allows the cutter links to rock rearwardly in a direction longitudinal to a longitudinal axis of the saw bar.